Based on the above discussion, one can evaluate the experimental sensitivity to axion-like dark matter.
We still need to know the sensitivity of the K magnetometer itself.
The \(^3\) He-K system has five orders smaller spin-destruction cross section than that of \(^{129}\) Xe-Rb sytems,
and thus the K magnetometer can still achieve a femtotesla sensitivity \(\sim \)\( 1~\textrm {fT} / \textrm {Hz}^{1/2}\) , as demonstrated in ref. [1]};
thus, the magnetic sensitivity based on \(^3\) He spin amplifier could probably reach \(1~\textrm {aT} / \textrm {Hz}^{1/2}\)  within the amplifier bandwidth.
We note that the experimental sensitivity to \(\rm {g}_{\rm {aNN}}\)  scales as \(t^{-1/2}\)  as a function of measurement time \(t\) .
When the measurement time is five hours,
the search sensitivity of \(|\textrm {g}_{\textrm {aNN}}|\)  can reach \( \sim \)\( 10^{-13}~\textrm {GeV}^{-1}\) ,
which improves over the astrophysical limit (from supernova SN1987A cooling [2]}, [3]}) by at least four orders of magnitude.
For dark photon-nucleon interactions,
the experimental sensitivity could reach \(\rm {g}_{\rm {dEDM}} \sim 10^{-17}\)  GeV\(^{-1}\)  and \(\rm {g}_{\rm {dMDM}} \sim 10^{-13}\)  GeV\(^{-1}\) ,
which are far beyond the astrophysical limits.
Using such a spin-based amplifier,
it is possible to explore new physics beyond the standard model.
